Author Topic: Matrices Question (Read 655 times) Tweet Share

skeletalclown · « **on:** August 26, 2014, 06:16:42 pm »

Okay, i've got a SAC coming up and i know there's going to be a question similar to this on it, but I just can't seem to ge tmy head around it???

a) The prices of the breads in a bakery have been changed. The S loaf went down by 10%, the M loaf went up by 20%, the L loaf went up by 10% and the XL loaf didn't change.
If the original prices are $1.40, $2.00, $2.50 and $3.10, Show the price changes in a 4 x 4 matrix called "Q".

We were also given the identity matrix:

[1 0 0 0]
[0 1 0 0]
[0 0 1 0]
[0 0 0 1]

b) Find the new prices of each loaf.

c) Given a certain number of each loaf is sold (my book is at school so i dont have the table with the numbers sold here, so jsut the process is fine), find out the profit.

plato · « **Reply #1 on:** August 26, 2014, 10:39:29 pm »

Column matrix for price change = $C= \left[ \begin{array}{c} \\0.9 \\1.2 \\1.1 \\1.0 \end{array} \right]$

Convert this into a square matrix $P=I \times C$

$P= \left[ \begin{array}{cccc} \\1 & 0&0&0 \\0 & 1 &0&0 \\0 & 0 &1&0 \\0&0&0&1 \end{array} \right] \times \left[ \begin{array}{c} \\0.9 \\1.2 \\1.1 \\1.0 \end{array} \right]= \left[ \begin{array}{cccc} \\0.9 & 0&0&0 \\0 & 1.2 &0&0 \\0 & 0 &1.1&0 \\0&0&0&1 \end{array} \right]$

P= modified price change matrix $= \left[ \begin{array}{cccc} \\0.9 & 0&0&0 \\0 & 1.2 &0&0 \\0 & 0 &1.1&0 \\0&0&0&1 \end{array} \right]$

Original price matrix $G= \left[ \begin{array}{c} \\1.40 \\2.00 \\2.50 \\3.10 \end{array} \right]$

New prices $PG= \left[ \begin{array}{c} \\1.26 \\2.40 \\2.75 \\3.10 \end{array} \right]$

Profit = Price - cost but there is no cost info

skeletalclown · « **Reply #2 on:** August 27, 2014, 12:41:55 am »

Thank you very much!

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